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As I understand, idealism is the view that the mind is fundamental and the body as well as the world we perceive are just derivatives of the mind. Is this right?
If so, if we had a hypothetical being, which could accept no sensory input (deaf, blind, no smell,...), but still had a brain, would an idealist say that the brain could still think?
Idealism does not necessarily assert mind as a fundamental entity, but it does assert the metaphysical priority of the ideal over the material. The view of reality as derivative from the mind is associated with a particular strain, so-called subjective idealism, the extreme form of which is solipsism, asserting that only a single mind exists, the subject's own.
However, one does not have to be a solipsist, or even an idealist, to believe that thinking can happen without a sensory input. There is a famous Avicenna's Floating Man thought experiment, where he asks us to imagine that a man is created suspended in the air, with all senses disabled:
"Then let the subject consider whether he would affirm the existence of his self. There is no doubt that he would affirm his own existence, although not affirming the reality of any of his limbs or inner organs, his bowels, or heart or brain or any external thing. Indeed he would affirm the existence of this self of his while not affirming that it had any length, breadth or depth. And if it were possible for him in such a state to imagine a hand or any other organ, he would not imagine it to be a part of himself or a condition of his existence".
According to Avicenna, this proves the possibility of existence of conscious and thinking disembodied soul. Avicenna himself was an idealist, but the experiment itself does not rest on idealism, and inspired many modern variations by non-idealist philosophers, for example Putnam's "brain in a vat".
In Leibniz's monadology each monad is unto itself, "without any doors or windows", receiving no sensory or any other input. Awareness of other monads only emerges due to "pre-established harmony". The thinking monads, souls, are at the top of the hierarchy.
Hegel was an idealist of a kind, yet he starts in the Phenomenology of Spirit with sense-certainty, before quickly moving on after examining it isn't sufficient in characterising how we understand the world and what the world is.
In Western Idealism, the empirical is sublated into the ideal, hence asserting the latter as a larger category than the former.
For any subjective idealist with a God, wouldn't He have to be such? There is no point in perceiving the results of your own being and intention. So God most likely has no use for senses and would have none.
There is also no point in an ideal being having a brain, per se, but if the brain is just where thinking happens, and thinking happens, we could see Him has having such, at least metaphorically.
Since this is a majority of idealists historically, and most such idealists then go on to imagine thoughts in the mind of God, your answer would have to be yes, almost always.
